Method and apparatus for generating and distributing satellite tracking information

ABSTRACT

A method and apparatus for generating and distributing satellite tracking data to a remote receiver is disclosed. The method for includes extracting from satellite-tracking data initial model parameters representing a current orbit of at least one satellite-positioning-system satellite, computing an orbit model using the initial model parameters, wherein a duration of the orbit model is longer than a duration of the satellite-tracking data, comparing, for an overlapping period of time, the orbit model to the satellite-tracking data; and adjusting the orbit model to match the satellite tracking data for the overlapping period of time so as to form an adjusted orbit model. The adjusted orbit model comprises the long-term-satellite-tracking data.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part application of co-pendingU.S. patent application Ser. No. 09/993,335, filed Nov. 6, 2001, whichis a continuation-in-part of U.S. patent application Ser. No.09/884,874, filed Jun. 19, 2001, now U.S. Pat. No. 6,560,534, which is acontinuation-in-part of U.S. patent application Ser. No. 09/875,809,filed Jun. 6, 2001, now U.S. Pat. No. 6,542,820. This applicationcontains subject matter that is related to co-pending U.S. patentapplication Ser. No. 09/715,860, filed Nov. 17, 2000, now U.S. Pat. No.6,417,801. Each of the aforementioned related patents and/or patentapplications is herein incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to generating satellite trackinginformation for earth orbiting satellites. More specifically, theinvention relates to a method and apparatus for generating anddistributing satellite tracking information through a network orcommunications link.

2. Description of the Related Art

A positioning receiver for the Global Positioning System (GPS) usesmeasurements from several satellites to compute a position. The processof acquiring the GPS radio signal is enhanced in speed and sensitivityif the GPS receiver has prior access to a model of the satellite orbitand clock. This model is broadcast by the GPS satellites and is known asan ephemeris or ephemeris information. Each satellite broadcasts its ownephemeris once every 30 seconds. Once the GPS radio signal has beenacquired, the process of computing position requires the use of theephemeris information.

The broadcast ephemeris information is encoded in a 900 bit messagewithin the GPS satellite signal. It is transmitted at a rate of 50 bitsper second, taking 18 seconds in all for a complete ephemeristransmission. The broadcast ephemeris information is typically valid for2 to 4 hours into the future (from the time of broadcast). Before theend of the period of validity the GPS receiver must obtain a freshbroadcast ephemeris to continue operating correctly and produce anaccurate position. It is always slow (no faster than 18 seconds),frequently difficult, and sometimes impossible (in environments withvery low signal strengths), for a GPS receiver to download an ephemerisfrom a satellite. For these reasons it has long been known that it isadvantageous to send the ephemeris to a GPS receiver by some other meansin lieu of awaiting the transmission from the satellite. U.S. Pat. No.4,445,118, issued Apr. 24, 1984, describes a technique that collectsephemeris information at a GPS reference station, and transmits theephemeris to the remote GPS receiver via a wireless transmission. Thistechnique of providing the ephemeris, or equivalent data, to a GPSreceiver has become known as “Assisted-GPS.” Since the source ofephemeris in Assisted-GPS is the satellite signal, the ephemerisinformation remains valid for only a few hours. As such, the remote GPSreceiver must periodically connect to a source of ephemeris informationwhether that information is received directly from the satellite or froma wireless transmission. Without such a periodic update, the remote GPSreceiver will not accurately determine position.

The deficiency of the current art is that there is no source ofsatellite trajectory and clock information that is valid for longer thana few hours into the future, and it can be expensive to send theephemeris information repeatedly to the many remote devices that mayneed it. Moreover, mobile devices may be out of contact from the sourceof the Assisted-GPS information when their current ephemeris becomesinvalid.

Therefore, there is a need in the art for a method and apparatus forproviding satellite trajectory and clock information that is valid foran extended period into the future, e.g., many days into the future.

SUMMARY OF THE INVENTION

The present invention is a method and apparatus for generating satellitetracking data (STD) that is valid for extend periods of time into thefuture, i.e., long term STD or LT-STD. The STD may contain futuresatellite trajectory information and/or satellite clock information. TheSTD is derived by receiving at one or more satellite tracking stationsthe signals from at least one satellite and determining satellitetracking information (STI) from the received signals. STI containspresent satellite orbit trajectory data and satellite clock information.

The STD may be provided to a remote satellite signal receiver via anetwork or communications system. The satellite system may include theglobal positioning system (GPS), GLONASS, GALILEO, or other satellitesystems that may use STD to enhance the performance of the receiver. Byusing the LT-STD, a remote receiver may accurately operate for dayswithout receiving an update of the broadcast ephemeris information asnormally provided from the satellites.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention are attained and can be understood in detail, a moreparticular description of the invention, briefly summarized above, maybe had by reference to the embodiments thereof which are illustrated inthe appended drawings.

It is to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 depicts a system for creating and distributing satellite trackingdata (STD) to remote GPS receivers;

FIG. 2 depicts a method for forming the STD from the satellitemeasurements made at satellite tracking stations;

FIG. 3 depicts a timeline of STD data that conforms to the broadcastephemeris format models as described in ICD-GPS-200C yet spans manyhours;

FIG. 4 depicts a flow diagram of a method that uses a least squaresestimation technique to update parameters in an orbit trajectory model;

FIG. 5 depicts the error in the orbit model derived from the STD, andcompares the error to the error in the broadcast ephemeris;

FIG. 6 depicts an example of a data table that could be used in an STDdatabase.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 depicts a block diagram of a system 100 for creating anddistributing satellite tracking data (STD). The satellite system mayinclude the global positioning system (GPS), GLONASS, GALILEO, or othersatellite systems that may use STD to enhance the performance of thereceiver. The following disclosure uses GPS as an illustrative systemwithin which the invention operates. From the following disclosure,those skilled in the art will be able to practice the invention inconjunction with other satellite systems.

A network of GPS tracking stations 102 is used to collect measurementdata from the GPS satellites 104. Such a network is described in detailin U.S. patent application Ser. No. 09/615,105, filed Jul. 13, 2000. Thenetwork could comprise several tracking stations that collect satellitetracking information (STI) from all the satellites in the constellation,or a few tracking stations, or a single tracking station that onlycollects STI for a particular region of the world. An STD collection andcomputation server 106 collects and processes the measurement data (thismeasurement data is referred to herein as satellite tracking information(STI) that includes at least one of: code phase measurements, carrierphase measurements, Doppler measurements, or ephemeris data). In thepreferred embodiment, measurement data is obtained from both the L1 andL2 frequencies on which the GPS satellites transmit. Alternativeembodiments may use only one of these frequencies, and/or otherfrequencies used by other satellite systems or by future versions of theGPS system. The server 106 produces: 1) accurate satellite tracking data(STD) (e.g., a trajectory of each satellite and/or a clock offsetmeasurement) during the data collection period, 2) a prediction of thefuture STD of each satellite, and 3) models that match the future STD ofeach satellite. The server 106 comprises a central processing unit (CPU)118, support circuits 122, and memory 120. The CPU 118 may be any one ofthe many CPUs available on the market to perform general computing.Alternatively, the CPU may be a specific purpose processor such as anapplication specific integrated circuit (ASIC) that is designed toprocess satellite tracking information. The support circuits 122 arewell known circuits such as clock circuits, cache, power supplies andthe like. The memory 120 may be read only memory, random access memory,disk drive storage, removable storage or any combination thereof. Thememory 120 stores executable software, e.g., LT-STD software 124, that,when executed by the CPU 118, causes the system 100 to operate inaccordance with the present invention.

The set of satellite trajectory and clock data produced by the LT-STDsoftware 124 constitutes the STD information, and is stored in an STDdatabase 108. A distribution server 110 accesses the database 108 togather the most recent set of data, formats the data using thetrajectory conversion software 111 according to the relevant interfacestandard, and distributes the formatted data to GPS devices 112 thatrequire satellite orbit information. The distribution process may be bysome form of wireless communications system 114, or over the Internet116, or a combination of both, or by some other means of communication.Once the GPS devices 112 have received the orbit data, they may operatecontinually for many days without needing to download fresh broadcastephemeris from the satellites or from any other source. The orbit datadistributed to the GPS devices may be in the same format as thebroadcast ephemeris or may be some other model format that is defined bythe GPS device. Herein this orbit data is generally referred to as asatellite tracking model (STM). The loading of the STM into the GPSreceiver can be accomplished in many ways. Using the cradle for apersonal digital assistant (PDA), direct connection to a network, or awireless technology, such as Bluetooth or a cellular network, are a fewexamples of how the ephemeris data can be transferred to the receiver.The transmission is generally accomplished by broadcasting the LT-STD(or a model representing all or a portion of the LT-STD) withoutknowledge of the specific location of the GPS receiver. As such, thedistribution server does not require the GPS receiver to send anyinformation through the network to the distribution server.

Since GPS is a ranging system in and of itself, the data transmitted bythe GPS satellites can be used to determine the range, range-rate andclock offsets to the GPS satellites from a set of tracking stations.This set of observations generated by the tracking stations 102 is usedin the orbit determination process, and in the estimation of thesatellite clock characteristics. The set of monitoring stations 102could be a single station, a public network such as the ContinuouslyOperating Reference System (CORS), or a privately owned and/or operatednetwork.

FIG. 2 illustrates the preferred embodiment of a process for computingLT-STD. The process begins at step 202 with the collection of satellitemeasurements from the network of tracking stations. Measurements such ascode phase, (CP), carrier phase (CPH), and Doppler may be used for GPSsatellite tracking information. At step 204, the measurements are usedto compute the satellite trajectories and clock offsets over the periodsduring which the data was collected. This step is performed usingstandard GPS processing techniques and software packages well known inthe art. Examples of this type of software are GIPSY from the JetPropulsion Laboratory (JPL), GEODYN from NASA Goddard Space FlightCenter (GSFC), and the commercial product, MicroCosm, from Van MartinSystems.

At step 206, the satellite trajectories and clock offsets from step 204are propagated into the future with the same software package, usingstandard orbit models, such as gravity, drag, solar radiation pressure,tides, third body effects, precession, nutation, and other conservativeand non-conservative forces effecting the satellite trajectory. Theseare normally the same force models that are used in the estimation ofthe satellite orbits during the data fit interval. A subset of thesemodels, such as those for drag and solar radiation pressure, areadjusted during the orbit estimation process described in step 204 tobest fit the trajectory. This combination of known and estimated forcemodels parameters is used in the propagation 206 to provide thepropagated orbit for time outside the data fit interval. The clockoffsets for GPS satellites are typically very small, and change linearlyover time. These clock offsets are propagated into the future usingstandard models, such as a second order model containing clock offset,drift, and drift rate.

At step 208, the propagated satellite trajectories and/or clock offsetsare stored as STD in a database. At step 210, the trajectory conversionsoftware converts the LT-STD data into a model and format expected bythe GPS device to which the model is to be provided. At step 212. theprescribed model or information is output. For use with existing GPSreceivers, the preferred embodiment of the model is the GPS ephemerismodel as described in ICD-GPS-200 and an ephemeris model is generatedfrom the LT-STD for each 4 hour period as illustrated in the timeline300 of FIG. 3, i.e., a different model 301, 302 and so on is generatedfor each six hour period. As such, the plurality of models 301, 302 andso on cumulatively span the length of the available LT-STD.

In an alternate embodiment, at step 204 (FIG. 2), the satellitetrajectories and clock offsets may be estimated using the data broadcastby the satellites and the standard equations given in ICD-GPS-200c.

The orbit model is a mathematical representation of the satellitetrajectory that describes the trajectory as a function of a small numberof variables and eliminates the need to provide satellite positionvectors explicitly as a table of time vs. satellite positions. Anexample of an ephemeris model is the classic six element Keplerianorbital model. Although this model lacks long term accuracy, it is afunctional ephemeris model for providing satellite trajectoryinformation as a function of a small number of variables. In thepreferred embodiment, the model used to describe the trajectory is GPSstandard ephemeris, specified in ICD-GPS-200c, following the sameconventions and units. This is the preferred method to provide maximumcompatibility with existing GPS receivers. However, other orbit modelscould also be used to represent the satellite trajectory. Orbit modelscan be selected to provide increased accuracy, longer duration fits,more compact representation of the trajectory, or other optimizationsrequired in an application.

This invention is different from the current art in that the orbit modelprovided to the GPS device is not the ephemeris data broadcast by theGPS satellites. Current art downloads the ephemeris broadcast from theGPS satellites and retransmits that data to GPS devices. In thisinvention, the broadcast ephemeris data is not required at any stage andis not used in the preferred implementation.

The broadcast ephemeris data provided by the GPS satellites cover aspecific time period (typically 4 hours) and the end of that time theinformation becomes unusable. For example, if a device receives abroadcast ephemeris that will expire in 5 minutes, the device would needthe new broadcast ephemeris before operating outside that 5 minuteinterval. With this invention, the STD may be formatted for the timeperiod required by the device. This time period may be for the currenttime forward or may be for some time interval in the future. Forexample, a device may request orbit information in the standard GPSephemeris format for the current time. In this case, the ephemerisprovided to the device would be valid for the next 6 hours. The devicecould request orbit information for the next 12 hours in the standardGPS format which could be supplied as two six hour ephemeris orbitmodels. In addition, different orbit models and formats that supportdifferent accuracies and standards can be generated from the LT-STD.

Fitting the LT-STD to the desired orbit model can be accomplished in anumber of mathematical methods. The preferred embodiment is aleast-squares fit of the orbit model parameters to the trajectory data.Other methods, such as Kalman filters or other estimators can also beused to obtain the orbit model parameters that best fit the trajectorydata. These techniques of fitting data to orbit models are well known topeople skilled in the art of orbit determination and orbit modeling.

The least squares technique provides an optimal fit of the trajectorydata to the orbit model parameters. FIG. 4 depicts a flow diagram of amethod of generating an orbit model using a least squares estimationtechnique. One embodiment of LT-STD is a table representation of time,position, and clock offset for each satellite, as shown in FIG. 6. Thetime, position, and clock offset can be in any time/coordinate system.For the purpose of simplicity and illustration, the time/coordinatesystem is GPS time and Earth-Centered-Earth-Fixed (ECEF) position in theWorld Geodetic Survey 1984 (WGS-84) reference frame.

At step 402, the STD for the desired time interval is extracted from theSTD database. The orbit model parameters are initialized to the orbitmodel values obtained by a similar process for the previous interval.This guarantees that the initial orbit model parameters are a good fitat least for the beginning of the desired time interval. The rest of theprocess 400 will ensure that the parameters are adjusted so that theybecome a good fit for the entire time interval.

In the preferred embodiment there are 15 orbital parameters to beadjusted:

-   -   Square root of semi-major axis (metersˆ½)    -   Eccentricity (dimensionless)    -   Amplitude of sine harmonic correction term to the orbit radius        (meters)    -   Amplitude of cosine harmonic correction term to the orbit radius        (meters)    -   Mean motion difference from computed value (radians/sec)    -   Mean anomaly at reference time (radians)    -   Amplitude of cosine harmonic correction term to the argument of        latitude (radians)    -   Amplitude of sine harmonic correction term to the argument of        latitude (radians)    -   Amplitude of cosine harmonic correction term to the angle of        inclination (radians)    -   Amplitude of sine harmonic correction term to the angle of        inclination (radians)    -   Longitude of ascending node of orbit plane at weekly epoch        (radians)    -   Inclination angle at reference time (radians)    -   Rate of inclination angle (radians/sec)    -   Argument of perigee (radians)    -   Rate of right ascension (radians/sec)        Although it will be readily apparent that more terms may be        used, for better fits, or, fewer terms may be used for a more        compact model.

At step 404, the orbit model is used to predict what the trajectorywould be, the predicted data is denoted the “Model Trajectory Data”(MTD). If the model were perfect, the MTD would coincide exactly withthe STD. At step 406, the MTD and OTD are compared to see how closelythe orbit model fits the orbit data. In the preferred embodiment, thecomparison step 406 is performed by summing the squares of thedifferences between each trajectory point in the OTD and thecorresponding point in the MTD, and comparing the resulting sum to athreshold. If the fit is “good”, the model parameters are deemed “good”and the process stops at step 410. If the fit is not good then the modelparameters are adjusted at step 408. There are many techniques wellknown in the art for adjusting model parameters to fit data. Forexample, in FIG. 5, the six-hour ephemeris model was adjusted to fit sixhours of OTD using a subspace trust region method based on theinterior-reflective Newton method described in Coleman, T. F., and Y.Li, “On the convergence of reflective Newton methods for large scalenonlinear minimization subject to bounds”, Mathematical Programming,Vol. 67, Number 2, pp. 189-224, 1994, and Coleman, T. F., and Y. Li, “Aninterior, trust region approach for nonlinear minimization subject tobounds”, SIAM Journal on Optimization, Vol. 6, pp. 418-445, 1996. Thereare standard computer packages, e.g., MATLAB Optimization Toolbox, thatmay be used to implement these methods.

Steps 404, 406 and 408 are repeated until the model parameters are foundthat fit the OTD well.

When fitting an orbit model to trajectory data, there are many choicesof which orbit model to choose. The preferred embodiment is to use orbitmodels with parameters that have been defined in well-known standards.In one embodiment, the ephemeris parameters defined in the GPS interfacecontrol document, ICD-GPS-200c, are used. The ICD-GPS-200c definitionincludes a bit that specifies a 4-hour fit or a 6-hour fit. Typically,the satellite data is broadcast in 4-hour fits and, by the time thisdata is obtained by the observer of the satellite, the data is oftennear the end of its fit interval. In one embodiment of the currentinvention, sequential 6 hour windows of STD are used to create 6-hourephemeris models, using the technique described in FIG. 4 and theaccompanying text. This produces a set of ephemeris models asillustrated in FIG. 3. Although these particular 6-hour models are notavailable without this invention, the models nonetheless are definedusing standard parameters (i.e. ICD-GPS-200c) and will be understood byany device that was designed to be compatible with said standard.

Alternatively, the transmission time for the model may be dynamicallydetermined in response to various transmission network characteristics,e.g., cellular telephone rate structures, data transmission bandwidths,low network utilization periods, low network congestion periods and thelike. Thus, the invention determines present value of the specificcharacteristics and compares the present value to a threshold. Inresponse to the comparison, the invention will transmit or not transmitthe model. For example, the invention may monitor the network trafficand determine the least congested time to transmit the model. Manywireless networks have time varying rates. For example, cellulartelephone use is often less expensive on weekends compared to mid-weekrates. A useful embodiment of the current invention is to create asatellite tracking model that is valid for the period betweeninexpensive rates (example: valid from one Saturday to the next), andtransmit the model during the time that the rate is inexpensive. Assuch, the model is transmitted for less cost than if the models weretransmitted during a peak rate period. Also, or as an alternative, onemay define and send the model to coincide with periods of low data useon the network—whether the network is wireless or not (e.g. theinternet). Those skilled in the art will realize that many othertransmission time optimization characteristics can be used to determinewhen it is best to transmit the model to the receiver(s).

FIG. 5 shows an example of Satellite Tracking Data (STD) that wasgenerated for a time interval of greater than six hours. Then, using thetechnique described by FIG. 4 and accompanying text, parameters of anICD-GPS-200c ephemeris model were adjusted to give a best fit to 6 hoursof the STD. The orbit modeled by this 6-hour ephemeris was then comparedto the true trajectory, and for comparison, the true trajectory was alsocompared to the orbit modeled by the broadcast ephemeris. The resultsare shown in FIG. 5, illustrating how the broadcast ephemeris losesvalidity while the ephemeris created by this invention maintains itsvalidity with approximately one meter of error.

The clock offset of GPS satellites is easily modeled by threeparameters. In the preferred embodiment, the measured clock offset ismodeled by the three parameters defined in ICD-GPS-200c. Theseparameters represent clock offset, drift, and drift rate. The parametersare adjusted in a similar way to the method 400 described above to givea model that best fits the measured data over the time interval.

Alternative embodiments may use longer fit intervals, such as 8, 14, 26,50, 74, 98, 122, or 146 hours for each ephemeris model. These fitintervals are envisaged in ICD-GPS-200c, but are seldom, if ever,available from the broadcast ephemeris. Under the current invention,models with these fit intervals may be generated even when the broadcastephemeris is limited to a 4-hour fit interval.

Alternative embodiments of the STD data may include observed satellitevelocity, acceleration, clock drift, or clock drift rate and these termsmay be used in the process of fitting a model in ways which are wellknown in the art.

Another embodiment of an orbit model uses the spare data bits in thecurrent ephemeris format of a conventional GPS signal to provideadditional model parameters that would improve the data fit over longtime intervals. For example, subframe 1 has 87 spare bits that areavailable for additional parameters. This technique allows for moreparameters to describe the orbital motion of the satellites withoutcompromising the standard data format. This new ephemeris model is basedon the current ephemeris model with additional correction terms used toaugment the model to support the longer fit intervals with greateraccuracy.

Yet another embodiment of an orbit model is to develop a new set oforbital parameters that describe the satellite orbit which aredifferent, in part or in their entirety, from the GPS ephemeris modelparameters. With the goal of making the fit interval longer, differentparameters may provide a better description of the satellite orbit. Thisnew set of parameters could be defined such that they would fit into theexisting data structures, however, their implementation and algorithmsfor use would be different.

Still a further embodiment of an orbit model would be to develop a newset of orbital parameters that would not fit into the existing GPSephemeris model format. This new set of parameters would be developed tobetter address the trade-off between the number of parameters required,the fit interval, and the orbit accuracy resulting from the model. Anexample of this type of ephemeris parameter set is Brouwer's theory thatcould be used as is or modified to account for GPS specific terms.Brouwer's theory as described in Brouwer, D. “Solution of the Problem ofArtificial Satellite Theory without Drag”, Astron J. 64: 378-397,November 1959 is limited to satellites in nearly circular orbits such asGPS satellites.

Another embodiment is to use a subset of the standard ephemerisparameters defined in ICD-GPS-200c. This approach is particularly usefulwhen bandwidth and/or packet size is limited in the communication linkthat will be used to convey the orbit model to the Remote GPS Receiver.In one such embodiment, the fifteen orbit parameters described above,and in ICD-GPS-200c, may be reduced to a subset of 9 parameters, bysetting all harmonic terms in the model to zero:

-   -   Square root of semi-major axis (metersˆ½)    -   Eccentricity (dimensionless)    -   Mean motion difference from computed value (radians/sec)    -   Mean anomaly at reference time (radians)    -   Longitude of ascending node of orbit plane at weekly epoch        (radians)    -   Inclination angle at reference time (radians)    -   Rate of inclination angle (radians/sec)    -   Argument of perigee (radians)    -   Rate of right ascension (radians/sec)        Process 400 is then executed using this subset of parameters.        This reduces the amount of data that must be sent to the Remote        GPS Receiver. The receiver can then reconstruct a standard        ephemeris model by setting the “missing” harmonic terms to zero.        There are a large number of alternative embodiments to reduce        the size of the data, while still providing a model that fits        the STD, including:    -   Removing parameters from the model, and replacing them with a        constant, such as zero—as done above—or some other predetermined        value, which is either stored in the Remote GPS Receiver or        occasionally sent to the receiver.    -   The resolution of the parameters may be restricted in the        process 400, this too reduces the amount of data that must be        sent to the mobile GPS receiver.    -   Parameters, which are similar among two or more satellites, may        be represented as a master value plus a delta, where the delta        requires fewer bits to encode; an example of this is the        parameter Eccentricity, which changes very little among        different GPS satellites.        Some of these approaches reduce the ability of the model to fit        the data over a period of time (e.g., six hours). In this case,        the fit interval may be reduced (e.g. to four hours) to        compensate.

While the foregoing is directed to the preferred embodiment of thepresent invention, other and further embodiments of the invention may bedevised without departing from the basic scope thereof, and the scopethereof is determined by the claims that follow.

1. A method for creating long-term-satellite-tracking data, the methodcomprising: a) extracting from satellite-tracking data initial modelparameters representing a current orbit of at least onesatellite-positioning-system satellite; b) computing an orbit modelusing the initial model parameters, wherein a duration of the orbitmodel is longer than a duration of the satellite-tracking data; c)comparing, for an overlapping period of time, the orbit model to thesatellite-tracking data; and d) adjusting the orbit model to match thesatellite tracking data for the overlapping period of time so as to forman adjusted orbit model, wherein the adjusted orbit model comprises thelong-term-satellite-tracking data.
 2. The method of claim 1, furthercomprising: iterating c) and d) until an error produced by c) is lessthan a threshold.
 3. The method of claim 1, wherein c) comprises:determining at least one difference between at least on point in theorbit model and at least one point in the satellite-tracking data;squaring the at least one difference to form a square of the at leastone difference; summing the square of the at least one difference toform at least one resulting sum; and comparing the at least oneresulting sum to a threshold.
 4. The method of claim 3, furthercomprising: iterating c) and d) in view of comparing the at least oneresulting sum to a threshold.
 5. The method of claim 1, wherein theduration the orbit model is four hours, and wherein the duration of theorbit model is more than four hours.
 6. The method of claim 5, whereinthe duration of the orbit model is six hours.
 7. The method of claim 1,wherein d) further comprises: using a subspace trust region method basedon the interior-reflective Newton method.
 8. The method of claim 1,wherein the orbit model comprises at least one of: square root of asemi-major axis, eccentricity, amplitude of a sine harmonic correctionterm to an orbit radius, amplitude cosine harmonic correction term to anorbit radius, mean motion difference, mean anomaly at a reference time,amplitude of a cosine harmonic correction to an argument of latitude,amplitude of a sine harmonic correction to the argument of latitude,amplitude of a cosine harmonic correction to an argument of inclination,amplitude of a sine harmonic correction to the argument of inclination,longitudinal of an ascending node of an orbit plane at a weekly epoch,inclination angle at a reference time, rate of inclination angle, andrate of right ascension and argument of perigee.
 9. The method of claim1, wherein the orbit model comprises a mathematical representation of asatellite trajectory.
 10. The method of claim 1, further comprising:receiving the satellite-tracking data from a worldwide-referencenetwork, wherein the worldwide-reference network comprises a pluralityof satellite-signal receivers.
 11. A apparatus for creating long termsatellite tracking data, the apparatus comprising: memory having storedtherein executable instructions; a processor operable to execute theexecutable instructions to: a) extract from satellite-tracking datainitial model parameters representing a current orbit of at least onesatellite-positioning-system satellite; b) compute an orbit model usingthe initial model parameters, wherein a duration of the orbit model islonger than a duration of the satellite-tracking data; c) compare, foran overlapping period of time, the orbit model to the satellite-trackingdata; and d) adjust the orbit model to match the satellite tracking datafor the overlapping period of time so as to form an adjusted orbitmodel, wherein the adjusted orbit model comprises the long termsatellite tracking data.
 12. The apparatus of claim 11, wherein theprocessor is further operable to execute the executable instructions to:iterate c) and d) until an error produced by c) is less than athreshold.
 13. The apparatus of claim 12, wherein the executableinstructions to c) comprise executable instructions to: determine atleast one difference between at least on point in the orbit model and atleast one point in the satellite-tracking data; square the at least onedifference to form a square of the at least one difference; sum thesquare of the at least one difference to form at least one resultingsum; and compare the at least one resulting sum to a threshold.
 14. Theapparatus of claim 13, wherein the processor is further operable toexecute the executable instructions to: iterate c) and d) in view ofexecuting the executable instructions to compare the at least oneresulting sum to a threshold.
 15. The apparatus of claim 11, wherein theduration the orbit model is four hours, and wherein the duration of theorbit model is more than four hours.
 16. The apparatus of claim 15,wherein the duration of the orbit model is six hours.
 17. The apparatusof claim 11, wherein the executable instructions to d) compriseexecutable instruction to: use a subspace trust region method based onthe interior-reflective Newton method.
 8. The apparatus of claim 11,wherein the orbit model comprises at least one of: square root of asemi-major axis, eccentricity, amplitude of a sine harmonic correctionterm to an orbit radius, amplitude cosine harmonic correction term to anorbit radius, mean motion difference, mean anomaly at a reference time,amplitude of a cosine harmonic correction to an argument of latitude,amplitude of a sine harmonic correction to the argument of latitude,amplitude of a cosine harmonic correction to an argument of inclination,amplitude of a sine harmonic correction to the argument of inclination,longitudinal of an ascending node of an orbit plane at a weekly epoch,inclination angle at a reference time, rate of inclination angle, andrate of right ascension and argument of perigee.
 19. The apparatus ofclaim 11, wherein the orbit model comprises a mathematicalrepresentation of a satellite trajectory.
 20. The apparatus of claim 11,wherein the processor is further operable to execute executableinstructions to: receive the satellite-tracking data from aworldwide-reference network, wherein the worldwide-reference networkcomprises a plurality of satellite-signal receivers.